Question

the half-life of radium-226 is 1600 years. suppose we have a 27-mg sample. (a) how much of the sample will remain after 4500 years? (round your answer to one decimal place.) mg (b) after how many years will only 15 mg of the sample remain? (round your answer to one decimal place.) yr

Answer 1

(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

The result is obtained by using the exponential decay equation.

What is the exponential decay equation?

The exponential decay equation can be used to calculate radioactive decay for the activity, the nuclei, and also the mass. The exponential decay equation for the mass is

$m = m_{o} e^{-\lambda t}$

Where

• m = the initial mass
• m₀ = the remaining mass
• λ = decay constant (0.693/T½)
• T½ = half-life
• t = decay time

The half-life of radium-226 is 1600 years and the mass of a sample is 27 mg.

(a) What is the remaining mass after 4500 years?

(b) What is the decay time if the remaining mass is 15 mg?

First, let's calculate the decay constant.

λ = 0.693/T½

λ = 0.693/1600

λ = 0,000433

After 4500 years, the remaining mass is

$m = m_{o} e^{-\lambda t}$

$m = 27 e^{-0.000433 \times 4500}$

m = 27 × 0.142

m = 3.8 mg

If the remaining mass is 15 mg, the decay time is

$m = m_{o} e^{-\lambda t}$

$15 = 27 e^{-0.000433 t}$

$ln \frac{15}{27} = ln (e^{-0.000433 t})$

$ln \frac{15}{27} = -0.000433 t$

-0.588 = - 0.000433t

t = 1357.9 years

Hence,

(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

Learn more about radioactive decay here:

brainly.com/question/9796067

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